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Total Surface Area of Star Pyramid given Chord Length Formula

GoTotal Surface Area of Star Pyramid Formula

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Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid. Check FAQs

TSA = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

TSA - Total Surface Area of Star Pyramid?l_c - Chord Length of Star Pyramid?l_e(Base) - Edge Length of Base of Star Pyramid?l_e(Lateral) - Lateral Edge Length of Star Pyramid?l_e(Ridge) - Ridge Length of Star Pyramid?

Total Surface Area of Star Pyramid given Chord Length Example

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Here is how the Total Surface Area of Star Pyramid given Chord Length equation looks like with Values.

Here is how the Total Surface Area of Star Pyramid given Chord Length equation looks like with Units.

Here is how the Total Surface Area of Star Pyramid given Chord Length equation looks like.

315.4173 = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

315.4173m² = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})

315.4173 = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

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Total Surface Area of Star Pyramid given Chord Length Solution

Follow our step by step solution on how to calculate Total Surface Area of Star Pyramid given Chord Length?

FIRST Step Consider the formula

TSA = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l c}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

Next Step Substitute values of Variables

∴

TSA = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{10m}^{2}}{2}) + (10 \cdot \sqrt{(\frac{6m + 11m + 8m}{2}) \cdot (\frac{11m + 8m - 6m}{2}) \cdot (\frac{6m - 11m + 8m}{2}) \cdot (\frac{6m + 11m - 8m}{2})})

Next Step Prepare to Evaluate

∴

TSA = (\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{10^{2}}{2}) + (10 \cdot \sqrt{(\frac{6 + 11 + 8}{2}) \cdot (\frac{11 + 8 - 6}{2}) \cdot (\frac{6 - 11 + 8}{2}) \cdot (\frac{6 + 11 - 8}{2})})

Next Step Evaluate

∴

TSA = 315.417348998167m²

LAST Step Rounding Answer

∴

TSA = 315.4173m²

Total Surface Area of Star Pyramid given Chord Length Formula Elements

Variables

Functions

Total Surface Area of Star Pyramid

Total Surface Area of Star Pyramid is the total amount of two-dimensional space occupied on all the faces of the Star Pyramid.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Star Pyramid

Chord Length of Star Pyramid

Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Star Pyramid

Edge Length of Base of Star Pyramid

Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Star Pyramid

Lateral Edge Length of Star Pyramid

Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.

Symbol: l_e(Lateral)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Lateral Edge Length of Star Pyramid

Ridge Length of Star Pyramid

Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.

Symbol: l_e(Ridge)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ridge Length of Star Pyramid

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Star Pyramid

Go Total Surface Area of Star Pyramid

TSA = (\frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot {(l e(Base) \cdot [phi])}^{2}}{2}) + (10 \cdot \sqrt{(\frac{l e(Base) + l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Lateral) + l e(Ridge) - l e(Base)}{2}) \cdot (\frac{l e(Base) - l e(Lateral) + l e(Ridge)}{2}) \cdot (\frac{l e(Base) + l e(Lateral) - l e(Ridge)}{2})})

How to Evaluate Total Surface Area of Star Pyramid given Chord Length?

Total Surface Area of Star Pyramid given Chord Length evaluator uses Total Surface Area of Star Pyramid = (sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))) to evaluate the Total Surface Area of Star Pyramid, Total Surface Area of Star Pyramid given Chord Length formula is defined as the total amount of two-dimensional space occupied on all the faces of the Star Pyramid and is calculated using the chord length, edge length of base, lateral edge length, and ridge length of the Star Pyramid. Total Surface Area of Star Pyramid is denoted by TSA symbol.

How to evaluate Total Surface Area of Star Pyramid given Chord Length using this online evaluator? To use this online evaluator for Total Surface Area of Star Pyramid given Chord Length, enter Chord Length of Star Pyramid (l_c), Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)) & Ridge Length of Star Pyramid (l_e(Ridge)) and hit the calculate button.

FAQs on Total Surface Area of Star Pyramid given Chord Length

What is the formula to find Total Surface Area of Star Pyramid given Chord Length?

The formula of Total Surface Area of Star Pyramid given Chord Length is expressed as Total Surface Area of Star Pyramid = (sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))). Here is an example- 315.4173 = (sqrt(5*(5-(2*sqrt(5))))*(10^2)/2)+(10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)*((6+11-8)/2))).

How to calculate Total Surface Area of Star Pyramid given Chord Length?

With Chord Length of Star Pyramid (l_c), Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)) & Ridge Length of Star Pyramid (l_e(Ridge)) we can find Total Surface Area of Star Pyramid given Chord Length using the formula - Total Surface Area of Star Pyramid = (sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Star Pyramid?

Here are the different ways to Calculate Total Surface Area of Star Pyramid-

Total Surface Area of Star Pyramid=((sqrt(5*(5-(2*sqrt(5))))*(Edge Length of Base of Star Pyramid*[phi])^2)/2)+(10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2)))

Can the Total Surface Area of Star Pyramid given Chord Length be negative?

No, the Total Surface Area of Star Pyramid given Chord Length, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Star Pyramid given Chord Length?

Total Surface Area of Star Pyramid given Chord Length is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Star Pyramid given Chord Length can be measured.

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Total Surface Area of Star Pyramid given Chord Length Formula

​GoTotal Surface Area of Star Pyramid Formula

Total Surface Area of Star Pyramid given Chord Length Example

Total Surface Area of Star Pyramid given Chord Length Solution

Total Surface Area of Star Pyramid given Chord Length Formula Elements

Other Formulas to find Total Surface Area of Star Pyramid

How to Evaluate Total Surface Area of Star Pyramid given Chord Length?

FAQs on Total Surface Area of Star Pyramid given Chord Length

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GoTotal Surface Area of Star Pyramid Formula